All bases have an exponent

Math Questions: Laws Of Exponents And Algebraic Fractions

Approved & Edited by ProProfs Editorial Team

The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.

Learn about Our Editorial Process

| By Tjkim

Tjkim

Community Contributor

Quizzes Created: 25 | Total Attempts: 77,032

Questions: 17 | Attempts: 3,554 | Updated: Mar 22, 2023

Quiz Flashcard

Questions

Settings

Feedback

During the Quiz End of Quiz

Difficulty

Sequential Easy First Hard First

Create your own Quiz

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

Laws of Exponents and Algebraic Fractions

Questions and Answers

1.
- A.
- B.
- C.
Correct Answer
A.
2.
- A.
- B.
- C.
Correct Answer
B.
3.

What is the answer to [(x ⁴ y ⁵)] ⁰

Correct Answer
one
1

Explanation
The given answer "one, 1" suggests that the expression [(x 4 y 5)] 0 evaluates to both the word "one" and the number 1. However, without any context or further information about the expression or the variables x and y, it is not possible to determine the exact meaning or value of the expression. Therefore, the explanation for this answer is not available.

Rate this question:
4.

All bases have an exponent
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
When a base has no exponent written it is assumed to be 1, thus all bases have an exponent even if none is written.

Rate this question:

6
5.

The result of simplifying the expression (x ³ y ⁴ ) ³ is
- A.
- B.
- C.
  
  Y
Correct Answer
A.

Explanation
Multiply the power of x by 3 from the outside of the expression to get x^9. Multiply the power of y by 3 from the outside to get y^12

Rate this question:
6.

x ⁴ x ³ will result in an exponent of

Correct Answer
7
seven

Explanation
The expression "x 4 x 3" can be simplified as "x^4 * x^3". When multiplying two powers with the same base, you add the exponents. In this case, the base is "x" and the exponents are 4 and 3. So, the sum of the exponents is 7, resulting in an exponent of 7 for the expression.

Rate this question:

2
7.

A³ x a² =
- A.
- B.
  
  A
- C.
Correct Answer
C.
8.

Ac⁴ x a³c² =
- A.
- B.
- C.
Correct Answer
A.

Explanation
The given expression "ac4 x a3c2" represents the multiplication of the terms "ac4" and "a3c2". In this expression, "ac4" means "a" multiplied by "c" multiplied by 4, and "a3c2" means "a" multiplied by 3 multiplied by "c" squared. To multiply these terms, we can multiply the coefficients (4 and 3) together to get 12, and multiply the variables (a and c) together to get "a" multiplied by "c". Therefore, the result of the expression is 12ac.

Rate this question:

2
9.

4a³ x 3a⁵ =
- A.
- B.
- C.
Correct Answer
C.

Explanation
The given expression can be simplified by multiplying the coefficients and adding the exponents of the variables. Therefore, 4a3 x 3a5 is equal to 12a8.

Rate this question:

3
10.
- A.
- B.
- C.
Correct Answer
A.
11.
- A.
  
  3a
- B.
- C.
Correct Answer
C.
12.
- A.
- B.
- C.
Correct Answer
B.
13.

(a⁴)⁶ =
- A.
- B.
- C.
Correct Answer
A.

Explanation
The given expression (a4)6 can be simplified by multiplying the two numbers within the parentheses first. Since there is no variable or operation between the parentheses and the number 4, we can assume that it is a multiplication operation. Therefore, (a4)6 is equivalent to 4 * 6, which is 24.

Rate this question:
14.

(2a³c⁵)³ =
- A.
- B.
- C.
Correct Answer
C.
15.
- A.
- B.
- C.
Correct Answer
A.
16.
- A.
- B.
  
  A
- C.
  
  C
Correct Answer
A.
17.

(3a⁴)² =
- A.
- B.
- C.
Correct Answer
A.

Explanation
The given expression, (3a4)2, can be simplified by first evaluating the exponent, which is 2. This means that the expression inside the parentheses, 3a4, needs to be squared. To square this expression, we multiply it by itself. So, (3a4)2 = (3a4) x (3a4) = 9a8.

Rate this question:

0